2 Calcul de Weyl et déformations
2nd microlocalisation and conical refraction
We study the propagation of microlocal analytic singularities for the microdifferential equations with conical refraction studied by R. Melrose and G. Uhlmann. We transform the equations to a simple canonical form 2-microlocaly through quantized bicanonical transformations by Y. Laurent.
A general class of Gevrey-type pseudo differential operators
A Lie Group Structure for Fourier Integral Operators.
A Lie Group Structure for Pseudodifferential Operators.
A microlocal F. and M. Riesz theorem with applications.
Consider, by way of example, the following F. and M. Riesz theorem for Rn: Let μ be a finite measure on Rn whose Fourier transform μ* is supported in a closed convex cone which is proper, that is, which contains no entire line. Then μ is absolutely continuous (cf. Stein and Weiss [SW]). Here, as in the sequel, absolutely continuous means with respect to Lebesque measure. In this theorem one can replace the condition on the support of μ* by a similar condition on the wave front set WF(μ) of μ, while...
A Remark on Invariant Pseudo-Differential Operators.
A semi-global Taylor formula for manifolds
A Wiener algebra for the Fefferman-Phong inequality
Algebras of pseudodifferential operators on complete manifolds.
An accuracy improvement in Egorov's theorem.
We prove that the theorem of Egorov, on the canonical transformation of symbols of pseudodifferential operators conjugated by Fourier integral operators, can be sharpened. The main result is that the statement of Egorov's theorem remains true if, instead of just considering the principal symbols in Sm/Sm-1 for the pseudodifferential operators, one uses refined principal symbols in Sm/Sm-2, which for classical operators correspond simply to the principal plus the subprincipal symbol, and can generally...
An Example on the Heisenberg Group Related to the Levy Operator.
An integral operator representation of classical periodic pseudodifferential operators.
Analyse micro-locale du noyau de Bergman
Analyse semi-classique de l'opérateur de Schrödinger sur la sphère
Analytic index formulas for elliptic corner operators
Spaces with corner singularities, locally modelled by cones with base spaces having conical singularities, belong to the hierarchy of (pseudo-) manifolds with piecewise smooth geometry. We consider a typical case of a manifold with corners, the so-called "edged spindle", and a natural algebra of pseudodifferential operators on it with special degeneracy in the symbols, the "corner algebra". There are three levels of principal symbols in the corner algebra, namely the interior,...
Applications harmoniques stables
Biinvariant Operators on Nilpotent Lie Groups.
Boundary value problems and layer potentials on manifolds with cylindrical ends
We study the method of layer potentials for manifolds with boundary and cylindrical ends. The fact that the boundary is non-compact prevents us from using the standard characterization of Fredholm or compact pseudo-differential operators between Sobolev spaces, as, for example, in the works of Fabes-Jodeit-Lewis and Kral-Wedland . We first study the layer potentials depending on a parameter on compact manifolds. This then yields the invertibility of the relevant boundary integral operators in the...
Calcul exponentiel des opérateurs microdifférentiels d'ordre infini. II
Soit un opérateur pseudodifférentiel (ou microdifférentiel) tel que soit aussi un opérateur pseudodifférentiel. Alors le symbole de s’ecrit avec un symbole . Pour la réciproque, si est un opérateur à symbole , il existe un opérateur tel que . Tous ces résultats reposent sur la théorie développée dans la Note I de cette série. Comme application, on obtient une condition suffisante d’inversibilité pour les opérateurs pseudodifférentiels d’ordre infini.